4 Year GTA - Data driven inverse techniques for object identification

About the Project

Open to UK Applicants only

Mathematics are offering 3 fully-funded Graduate Teaching Assistant (GTA) PhD studentships available for UK applicants, starting in September 2026.

Graduate Teaching Assistantships allow research students to fund their PhD through part-time teaching work with the University.

A Graduate Teaching Assistant is responsible to the Head of School and is expected to undertake teaching or other duties within the School - not normally exceeding 8-10 contact hours per week - while undertaking research leading to a PhD.

Approximately 80% of their time will be spent on their doctoral research and 20% on their GTA responsibilities. Training is provided to help Graduate Teaching Assistants develop their teaching related skills and enhance their professional competencies.

Project Highlights

• Use established high-fidelity accelerated computational models to efficiently establish economical characterisations of hidden objects and data-dictionaries
• Develop new types of object features, apply clustering algorithms and assess accuracies of these features in classification approaches for object identification
• Work on a project, which has real-world applications in security screening, medical imaging, geophysical surveys, non-destructive testing, materials characterisations and archaeology.

Project description

Inverse problems involve the identification and location of hidden small inclusions from field measurements. New and novel approaches are needed since the field data can only be measured at limited locations and the data is typically noisy and incomplete. For many applications, a rapid decision about the location, shape and material properties of the inclusion is also demanded.

Traditional approaches to the solution of inverse problems involve setting up a functional to be minimised that expresses the difference between measured data and parameterised predicted measurements obtained from the solution of a (set of) partial differential equations (PDEs). The parameters sought typically relate to a discretisation of the material parameters. The approach is expensive (as it requires repeated solution of PDEs and many iterations and can suffer from non-uniqueness). Regularisation may be added, but its choice is often not straightforward.

This project considers an alternative approach in which the PDE model is replaced by a frequency dependent tensor characterisation model. Such characterisations can be easily found from field measurements and avoid a challenging functional minimisation procedure. Computational tools for computing the characterisations of surrogate objects are also available. The approach can be applied to a range of PDEs and have applications including medical imaging, understanding ground conditions, non-destructive testing, materials characterisations of composite materials and archaeology.

Key challenges remain as to how best to identify information about the hidden object from the data. To address this, this project will firstly develop large dictionaries of surrogate object characterisations using existing computational tools. Secondly, it will obtain and explore new object features and the extent to which these group characterisations of similar objects by using state-of-the-art clustering approaches. Thirdly, develop probabilistic classifiers, built on the dictionaries of computed characterisations, to provide a data-driven approach to object identification.

Project enquiries to Professor Paul Ledger Pdl11@leicester.ac.uk

Application enquiries to pgrapply@le.ac.uk

To apply please refer to the application advice and use the application link athttps://le.ac.uk/study/research-degrees/funded-opportunities/maths-gta

Start 21 September 2026

Funding Notes

The 4 year GTA funded studentships provide:

• A combined teaching and stipend payment, currently. for 2026/7 this will be £21,805 per year, paid in monthly instalments
• Tuition fees at UK rates

References

[1] H. Ammari and H. Kang, Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory, Springer 2007
[2] P.D. Ledger and W.R.B. Lionheart, The spectral properties of the magnetic polarizability tensor for metallic object characterisation. Mathematical Methods in the Applied Sciences, 2020; 43: 78–11.
[3] J. Elgy and P.D. Ledger, Efficient computation of magnetic polarizability tensor spectral signatures for object characterisation in metal detection. Engineering Computations, 2024; 41: 2472-2503.
[4] P.D. Ledger, W.R.B. Lionheart and J. Elgy, How far are two symmetric matrices from commuting? With an application to object characterization and identification in metal detection. Mathematical Methods in the Applied Sciences, 2026; 49: 1914–1942.